Uncovered interest parity and policy behavior: new evidence

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1 Economics Leers 69 (000) locae/ econbase Uncovered ineres pariy and policy behavior: new evidence Michael Chrisensen* The Aarhus School of Business, Fuglesangs Alle 4, DK-810 Aarhus V., Denmark Received 10 May 1999; received in revised form 3 March 000; acceped 5 April 000 Absrac McCallum [J. Mone. Econ. 33 (1994) ] inroduces policy behavior o resolve previous empirical rejecions of he uncovered ineres pariy (UIP) heory. In his noe, we reexamine his policy behavior argumen. Firs, we exend he daa se used by McCallum o include he recen 8 years, and conrary o he analysis provided by McCallum, we make a horough economeric analysis of his UIP specificaion. I is shown ha in mos cases his heory is suppored by he daa as well as i passes convenional economeric ess. We hen ake a closer look a his policy behavioral relaionship, bu unforunaely i urns ou ha his specificaion is inconsisen wih he UIP specificaion suggesed by McCallum. 000 Elsevier Science S.A. All righs reserved. Keywords: Uncovered ineres pariy; Policy behavior JEL classificaion: F31; E58 1. Inroducion The uncovered ineres pariy (UIP) heory saes ha differences beween ineres raes across counries can be explained by expeced changes in currencies. An expeced depreciaion of Deusche Mark agains he US Dollar, say, raises German ineres raes compared o US ineres raes in order o compensae American invesors for he expeced currency loss. Empirically, he UIP heory is usually rejeced assuming raional expecaions, and explanaions for his rejecion include ha expecaions are irraional (see Frankel and Froo, 1990; Mark and Wu, 1998), or ha ime-varying risk premia are presen (see Domowiz and Hakkio, 1985; Nieuwland e al., 1998), respecively. A hird explanaion was provided by McCallum (1994a), who observes ha regressing he change in spo exchange raes on he forward premium, one ypically finds a negaive *Tel.: ; fax: address: mic@asb.dk (M. Chrisensen) / 00/ $ see fron maer 000 Elsevier Science S.A. All righs reserved. PII: S (00)0090-1

2 8 M. Chrisensen / Economics Leers 69 (000) regression parameer of 4o3conrary o he expeced parameer of 1 1. McCallum argues, however, ha his finding may be consisen wih he UIP heory, if one inroduces policy behavior. Assuming policymakers adjus ineres raes in order o keep exchange raes sable, and ha hey are ineresed in smoohing ineres rae movemens, McCallum derives a reduced form equaion for he 1 spo exchange rae under raional expecaions. In fac, his resuls in a negaive heoreical relaionship beween he change in he spo exchange rae and he forward premium consisen wih his empirical findings. In his noe we analyze his hypohesis in furher deail. Firs, we reesimae he UIP relaionship for he exended sample period m o m and o a grea exen we confirm he resuls obained by McCallum for he period m o m. One criicism, which can be raised owards he analysis in McCallum (1994a), is, however, ha McCallum did no provide a sound economeric analysis of his empirical resuls. In order o verify his UIP heory empirically, we provide a number of convenional economeric ess, and surprisingly i urns ou ha he UIP specificaions esimaed pass hese ess, hereby lending suppor o he heory. To provide a final es of his UIP heory, we hen esimae he policy reacion funcion suggesed by McCallum in order o compare he esimaes of his relaionship and he esimaes obained from he UIP specificaion. Unforunaely, his es rejecs he UIP heory based on policy behavior.. UIP and policy behavior The UIP heory can be esed empirically by regressing he expeced change in he spo exchange rae on he forward premium as: Es s 5 f s j 11 (1) where s is he naural log of he spo exchange rae, f is he naural log of he forward rae, and Es 11 is he raional expecaion a ime of he log spo exchange rae o prevail a ime 1 1 based on he informaion se I. The forward premium f s is assumed o equal he ineres rae differenial according o covered ineres pariy, i.e. ( f s ) 5 (R R * ), where R and R* are he nominal ineres raes in he home and he foreign counries, respecively. Finally, j reflecs he expecaional error as well as oher influences ha keep s5 Es 11 ( f s ) from holding exacly. Under he raional expecaion hypohesis, McCallum derives he following regression equaion: s s 5 a 1 b( f s ) 1 j () where b 5 1 is required o confirm he UIP heory, and a is a measure of a consan risk premium. In Table 1 we presen he esimaion resuls obained from Eq. () using spo and 30-day forward exchange raes colleced from he Bank for Inernaional Selemens (BIS). The esimaes in Table 1 are almos similar o he resuls found by McCallum (1994a), besides from he esimae of b for $/DM, which is insignifican here. However, in all cases he esimae of b is significanly differen from he expeced value of 11, hereby rejecing he radiional UIP heory. 1 Kugler (000) generalizes his resul by making he policy reacion funcion dependen on he erm srucure spread.

3 M. Chrisensen / Economics Leers 69 (000) Table 1 OLS esimaion resuls obained from Eq. () (sample period: January 1978 March 1999) a * * (0.005) (0.003) (0.0031) b *.6940* (0.8976) (0.978) (0.8958) R S.E DW * Indicaes significance a he 5% level. Whie heeroskedasiciy-consisen sandard errors in parenheses. To explain his phenomenon McCallum argues ha if he policy maker is ineresed in smoohing ineres raes and uses ineres raes o keep exchange raes sable, he policy reacion funcion would look like : (R R * ) 5 F(R1 R 1 * ) 1 l(s s 1) 1 j (3) where z is a whie noise error erm, and 0, s # 1, l. 0 by assumpion. McCallum argues ha in order o make sure ha he forward premium does no become pure whie noise, he disurbance erm j11 in Eq. () canno be whie noise, and insead he suggess an AR(1) process given by: j 5 rj 1 u uru, 1.0 (4) 1 Combining Eqs. (1), (3) and (4) using covered ineres pariy and assuming raional expecaions, McCallum hen derives he following reduced form equaion for he exchange rae: r s 1 1 s s1 5 a 1 ]] ( f1 s 1) ] z1]]]] u (5) l l l1 s r and on his basis McCallum concludes ha Eq. (5) may be consisen wih he UIP relaionship in Eq. (). In fac, McCallum suggess ha s is close o 1, l is close o 0., and for values of r < 1, a negaive parameer o ( f s ), in accordance wih he empirical findings in Table 1 will appear. To verify his resul empirically, one has o es he esimaed regressions in Table 1 econo- merically. The es saisics (R, S.E. and DW) provided by McCallum and presened in Table 1 are no sufficien o validae he UIP heory empirically. Secion 3, herefore, provides a number of more advanced es saisics. Furhermore, o confirm he b esimaes in Table 1, he esimaes of s and l mus be consisen wih hese b esimaes. As a final es of Eq. (5), we hen esimae Eq. (3) in Secion 4. In McCallum (1994b) and Kugler (1997) he policy reacion funcion is made dependen on he erm srucure spread, and Hsu and Kugler (1997) show empirically ha he erm spread has a significan influence on US shor raes afer 1987.

4 84 M. Chrisensen / Economics Leers 69 (000) Table a Phillips Perron uni roos ess (sample period: January 1978 March 1999) s s f s * a The 5% criical value is * For $/Yen he criical 5% value is Economeric evidence To analyze he validiy of he regressions in Table 1, we firs es wheher he variables s s1 and f s are saionary. In Table we presen he resuls of he Phillips Perron uni roos es. 1 1 From Table we infer ha all variables seem o be saionary a he 5% level lending suppor o he OLS regressions in Table 1. To confirm his conclusion we will in addiion provide a number of misspecificaion ess. In Table 3 we presen he Ljung Box Q-saisic for 1h-order serial correlaion, he Jarque Bera normaliy es, he ARCH es for 1h-order condiional heeroskedasiciy, and wo Chow ess; one esing for a srucural break in Ocober 198, where moneary policy 4 was changed significanly in he US and he Unied Kingdom, and one esing for a srucural break in July 1993, where Chairman Greenspan indicaed ha he Federal Reserve would no longer use moneary arges as guidelines for is moneary policy. Table 3 indicaes ha he regressions in Table 1 pass all ess performed besides he normaliy es, which is suppored only for $/DM a he 1% level. We can, herefore, conclude ha hese relaions seem o be well specified economerically being fairly sable wihou exhibiing serial correlaion or 5 heeroskedasiciy. 3 Table 3 Misspecificaion es probabiliies (sample period: January 1978 March 1999) Q(1) Jarque Bera ARCH(1) Chow Chow Concerning saionariy he f s variable for he $/Yen is criical. Therefore, for his variable saionariy has been esed by an Augmened Phillips Perron es including an inercep erm. 4 In Ocober 198 moneary policy was changed from conrolling money o conrolling ineres raes in he US and he Unied Kingdom. 5 This evidence does no lend suppor o McCallum s predicion ha j follows an AR(1) process.

5 4. The policy reacion funcion M. Chrisensen / Economics Leers 69 (000) To reconcile he b esimaes in Table 1 wih he underlying srucural parameers of he policy reacion funcion given by Eq. (3), a final es of McCallum s policy behavioral UIP heory would be o esimae hese srucural parameers. One would imagine ha if he policy behavior argumen pu forward by McCallum is he soluion o he usual rejecions of he radiional UIP heory, Eqs. () and (5) would be subjec o he Lucas criique. However, in he previous secion he UIP relaionships were found o be raher sable and independen of major changes in moneary policy during he period analyzed, i.e. hey escape he Lucas criique. Obviously, his evidence is inconsisen wih he heoreical argumen provided by McCallum (1994a). Esimaing Eq. (3) wo problems arise. One is ha for all hree currencies we find ha a srucural break can be idenified in Ocober 198, where moneary policy was changed significanly in he US 6 and he Unied Kingdom. This evidence indicaes ha he UIP specificaions in Table 1 may be incorrec, since no srucural break can be idenified (see Table 3). The oher problem is due o severe heeroskedasiciy in he residuals for all hree currencies. Alhough he OLS esimaes provide appropriae inference, as long as we use Whie s heeroskedasiciy-consisen sandard errors, we will ry o correc for heeroskedasiciy when esimaing Eq. (3). Using differen GARCH models we are in fac able o obain reasonable specificaions for he policy reacion funcion. However, i is worh menioning ha he srucural parameers and heir sandard errors are almos idenical o he OLS esimaes, and herefore he ARCH parameers are no 7 8 repored. Again we follow McCallum, assuming ha covered ineres pariy holds, and Table 4 Table 4 ML esimaion resuls obained from Eq. (3) (sample period: January 1978 March 1999) GARCH(,) E-GARCH E-GARCH a * (0.000) (0.000) (0.000) s 0.981* 0.960* 0.968* (0.014) (0.07) (0.013) l 0.003* 0.00** (0.001) (0.001) (0.001) R Q(1) Jarque Bera ARCH(1) b 5s/l *, ** Indicae significance a he 5% and he 10% levels, respecively. 6 The 5% probabiliy is 0.000, and 0.08 for $/DM, $/ and $/Yen, respecively. 7 These resuls can be obained from he auhor upon reques. 8 In he case of $/Yen, a MA(1) erm has been included in order o correc for serial correlaion.

6 86 M. Chrisensen / Economics Leers 69 (000) presens he esimaes of he underlying srucural parameers in he policy reacion funcion given by Eq. (3). The maximum likelihood esimaes are obained using he Marquard algorihm in E-Views, and we infer ha a GARCH (,) process performs bes for he $/DM, whereas for $/ and $/Yen an E-GARCH process is mos appropriae. From Table 4 we infer ha for each currency he policy reacion funcion seems o be well specified. The goodness-of-fi is high and he residuals are no exposed o serial correlaion or any remaining heeroskedasiciy. Concerning he srucural parameers, we find ha five of six are significanly differen from zero, and in paricular we noice ha he s and l parameers are almos idenical across he hree currencies analyzed. s is close o 1 and l is negaive and very small alhough significanly differen from zero. Table 4 also presens a Wald es of McCallum s hypohesis ha b 5s/l assuming r 50 in Eq. (5), bu unforunaely we see ha his hypohesis is rejeced in all cases, hereby rejecing he policy behavioral UIP heory suggesed by McCallum. McCallum (1994a) prediced correcly ha s would be close o 1, bu his inuiion ha l50.0 canno be confirmed for any of he currencies analyzed. In fac, l is found o be negaive, which is inconsisen 9 wih Eq. (3). This conclusion holds irrespecive of he esimae of r as long as r, 1, which 10 McCallum assumes. 5. Conclusions By inroducing a policy reacion funcion, McCallum (1994a) deermines a UIP relaionship, which seems o be consisen wih mos empirical findings, and hereby McCallum has provided a promising soluion o previous rejecions of UIP. However, McCallum (1994a) did no provide an explici esimae of his policy reacion funcion. In his noe we have analyzed he modified UIP heory suggesed by McCallum (1994a) boh from an economeric and an economic poin of view. Economerically, we find ha $/DM, $/ and $/Yen for he period m o m behave amazingly well according o he modified UIP heory developed by McCallum. Unforunaely, i urns ou ha when we esimae he policy reacion funcion, we find a well-specified relaionship, whose srucural parameers are inconsisen wih he UIP relaionships esimaed. Acknowledgemens Helpful commens from an anonymous referee are graefully acknowledged. References Domowiz, I., Hakkio, C.S., Condiional variance and he risk premium in he foreign exchange marke. Journal of Inernaional Economics 19, A srucural break can be idenified in Ocober 198, bu regressions for he pre and pos Ocober 198 periods do no aler his conclusion. In none of hese sub-periods l becomes significanly posiive. 10 If one includes an AR(1) process in Eq. () (Table 1), he r parameer becomes insignifican for all hree counries.

7 M. Chrisensen / Economics Leers 69 (000) Frankel, J.A., Froo, K. (Eds.), Exchange rae forecasing echniques, survey daa, and implicaions for he foreign exchange marke. Working paper NBER. Hsu, C., Kugler, P., The revival of he expecaions hypohesis of he US erm srucure of ineres raes. Economics Leers 55, Kugler, P., Cenral bank policy reacion and he expecaions hypohesis of he erm srucure. Inernaional Journal of Finance and Economics (3), Kugler, P., 000. The expecaions hypohesis of he erm srucure of ineres raes, open ineres pariy and cenral bank policy reacion. Economics Leers 66, Mark, N.C., Wu, Y., Rehinking deviaions from uncovered ineres pariy: he role of covariance risk and noise. The Economic Journal 108, McCallum, B.T., 1994a. A reconsideraion of he uncovered ineres pariy relaionship. Journal of Moneary Economics 33, McCallum, B.T. (Ed.), 1994b. Moneary policy and he erm srucure of ineres raes. Working paper no NBER. Nieuwland, F.G.M.C., Verschoor, W.F.C., Wolff, C.C.P., EMS exchange rae expecaions and ime-varying risk premia. Economics Leers 60,